Efficiently maintain nonlinear graph neural networks for changing networks
Efficient Dynamic Algorithms for Graph Neural Networks with Non-Linear Propagation
Machine LearningData Structures and Algorithms
Summary
Graphs, which are networks of connected points, often change over time by adding or removing connections. The authors show how to quickly update the understanding of these changing networks using a type of AI called graph neural networks that involve nonlinear calculations. Their method avoids redoing all the work from scratch whenever the graph changes. This approach works well in theory and improves accuracy in real-world tests, making it practical for networks that evolve quickly.
What this means in practice
- •For network engineers: Update models of communication networks rapidly after connection changes to maintain accurate performance predictions.
- •For social media platform developers: Keep user influence or recommendation scores current despite users adding or removing friendships or follows.
Authors
Kiarash Banihashem, MohammadTaghi Hajiaghayi, Mahdi JafariRaviz, Silvio Lattanzi, Danny Mittal
Abstract
Graph Neural Networks (GNNs) are widely used for representation learning on graphs, but most methods assume static topologies, making them inefficient on evolving networks where edges change over time. Existing dynamic approaches either model graph evolution through temporal GNN architectures without focusing on efficient dynamic maintenance, or are restricted to linear propagation models based on Personalized PageRank. In this work, we study how to efficiently maintain node representations for non-linear GNN propagation under edge insertions and deletions. The propagation has no learned parameters, and only a classifier applied afterward is trained. For a broad class of standard activation functions, we develop a residual-based dynamic algorithm that selectively propagates local errors via push operations, maintaining an approximation to the evolving fixed point without full recomputation. We prove that our method achieves amortized $O(1/ε)$ update time per graph change under a degree-normalized error guarantee. Our approach uses a potential-based analysis in a degree-scaled norm and, in contrast to prior work on the linear case, requires no randomness assumptions on either the update sequence or the input vector. For the linear special case, we additionally provide an exact dynamic algorithm via low-rank matrix inverse updates. Experiments on benchmark datasets show that incorporating non-linearity improves accuracy while preserving efficient update performance, yielding a scalable and theoretically grounded method for maintaining this propagation on dynamic graphs.